Finite Group Databasebeta

← #44470545

Subgroups — #44470545

Order 29888.

330 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#21418742C211yesmaximal, characteristic, complemented
2C22×C4×D467C211yesmaximal, characteristic, complemented
3#28417936C211yesmaximal, characteristic, complemented
4#28417931C212yesmaximal, complemented
5#28417926C212yesmaximal, complemented
6#28417923C211yesmaximal, characteristic, complemented
7#28417921C211yesmaximal, characteristic, complemented
8#28417915C212yesmaximal, complemented
9(C22⋊D467)⋊C4C212yesmaximal, complemented
10#28417909C211yesmaximal, characteristic, complemented
11#123×C467C211yesmaximal, characteristic, complemented
12C23×D467C2211yescharacteristic
13#21418742—24no—
14C2×Dic934C2211yescharacteristic, complemented
15C2×D1868C2212yes—
16C2×C22⋊D467C2212yes—
17C2×C22⋊D467C2211yescharacteristic
18C2×C22⋊D467C2211yescharacteristic, complemented
19C22×Dic467C2211yescharacteristic
20C22×Dic467C2211yescharacteristic, complemented
21C2×C4×D467—24no—
22C2×C4×D467C2212yes—
23C2×C4×D467C2212yes—
24C2×C4×D467C2211yescharacteristic, complemented
25Dic467⋊C4C2212yescomplemented
26Dic467⋊C4C2212yescomplemented
27C22⋊Dic467C2211yescharacteristic
28(C2×D467)⋊C4C2212yes—
29(C2×D467)⋊C4C2212yes—
30(C2×D467)⋊C4C2212yescomplemented
31C4×Dic467C2212yescomplemented
32C2×D4×C467C2211yescharacteristic
33C22×C4×C467C2211yescharacteristic
34C4⋊C4×C467C2212yescomplemented
35C22⋊C4×C467C2211yescharacteristic
36C22⋊C4×C467C2212yescomplemented
37C22×D467—22no—
38C22×D467—24no—
39C22×D467C2311yescharacteristic
40C22×D467C2312yes—
41Dic934—22no—
42D1868—24no—
43C22⋊D467—22no—
44C22⋊D467—24no—
45C22⋊D467—22no—
46C2×Dic467—22no—
47C2×Dic467D414yescomplemented
48C2×Dic467C2312yes—
49C2×Dic467C2311yescharacteristic
50C2×Dic467C2311yescharacteristic
51C2×Dic467C2311yescharacteristic
52C4×D467—24no—
53C4×D467—24no—
54C4×D467—22no—
55C23×C467C2311yescharacteristic
56C23×C467C2311yescharacteristic
57D4×C467—22no—
58C2×C4×C467—22no—
59C2×C4×C467C2312yes—
60C2×C4×C467C2312yes—
61C2×C4×C467C2311yescharacteristic
62C22×C467—22no—
63C22×C467—21no—
64C22×C467—22no—
65C22×C467C2×D412yes—
66C22×C467C2411yescharacteristic
67C2×D467—28no—
68C2×D467—22no—
69C2×D467—22no—
70C2×D467—21no—
71C2×D467—22no—
72C2×D467#4114yescomplemented
73C4×C467—22no—
74C4×C467—21no—
75C4×C467—22no—
76Dic467—21no—
77Dic467—22no—
78Dic467C2×D412yes—
79Dic467C2×D412yes—
80C2×C467—22no—
81C2×C467—41no—
82C2×C467C22×D411yescharacteristic
83C2×C467C2×#4112yes—
84D467—24no—
85D467—41no—
86C467#52511yescharacteristic, complemented, Sylow
87#525—4671nomaximal, Sylow
88C2×#41—4671no—
89C23×C4—4671no—
90#123—4671no—
91#123D46711yescharacteristic, complemented
92C22⋊Q8—4672no—
93#121—4672no—
94#120—4671no—
95#120—4671no—
96C4×D4—4672no—
97C4×D4—4672no—
98#117—4671no—
99C24—4671no—
100#41—9344no—
101C2×Q8—4671no—
102C2×D4—4672no—
103C2×D4—4671no—
104C2×D4—4671no—
105C2×D4—4672no—
106C2×D4C2×D46711yescharacteristic
107C22×C4—9344no—
108C22×C4—4671no—
109C22×C4—4672no—
110C22×C4—4671no—
111C22×C4—4672no—
112C22×C4—4671no—
113C22×C4C2×D46711yescharacteristic
114C4⋊C4—4672no—
115C4⋊C4—4672no—
116C4⋊C4C2×D46712yescomplemented
117C22⋊C4—4671no—
118C22⋊C4—4672no—
119C22⋊C4—4672no—
120C22⋊C4—4672no—
121C22⋊C4C2×D46711yescharacteristic
122C22⋊C4C2×D46712yescomplemented
123C42—4672no—
124C23—9344no—
125C23—9342no—
126C23—4671no—
127C23—4672no—
128C23C22×D46711yescharacteristic
129C23C22×D46711yescharacteristic
130Q8—9342no—
131D4—22no—
132D4—9344no—
133D4—9344no—
134D4—9342no—
135D4—9342no—
136C2×C4—22no—
137C2×C4—9344no—
138C2×C4—9344no—
139C2×C4—9342no—
140C2×C4—9342no—
141C2×C4—4672no—
142C2×C4—4671no—
143C2×C4—4674no—
144C2×C4—4671no—
145C2×C4—4671no—
146C2×C4C22×D46712yes—
147C2×C4C22×D46711yescharacteristic
148C2×C4C22×D46712yes—
149C22—22no—
150C22—21no—
151C22—22no—
152C22—9348no—
153C22—9341no—
154C22—9342no—
155C22—9342no—
156C22—9342no—
157C22—4674no—
158C22D4×D46712yes—
159C22C23×D46711yescharacteristic
160C4—22no—
161C4—21no—
162C4—22no—
163C4—9341no—
164C4—9342no—
165C4—4672no—
166C4—4672no—
167C2—22no—
168C2—41no—
169C2—18681no—
170C2—9344no—
171C2C2×D4×D46711yescharacteristic
172C2#41×D46712yes—
subgroupG/H
center, FrattiniC22C23×D467
commutator, socle, cosocleC22×C467C24
Fitting#123×C467C2
hypercenter#123D467
hypocenterC467#525
LCSG ▷ C22×C467 ▷ C467
UCSC1 ◁ C22 ◁ #123

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#21418742C2semidirect
2. C22×C4×D467C2semidirect
3. #28417936C2semidirect
4. #28417931C2semidirect
5. #28417926C2semidirect
6. #28417923C2semidirect
7. #28417921C2semidirect
8. #28417915C2semidirect
9. (C22⋊D467)⋊C4C2semidirect
10. #28417909C2semidirect
11. #123×C467C2semidirect
14. C2×Dic934C22semidirect
18. C2×C22⋊D467C22semidirect
20. C22×Dic467C22semidirect
24. C2×C4×D467C22semidirect
25. Dic467⋊C4C22semidirect
26. Dic467⋊C4C22semidirect
30. (C2×D467)⋊C4C22semidirect
31. C4×Dic467C22semidirect
34. C4⋊C4×C467C22semidirect
36. C22⋊C4×C467C22semidirect
47. C2×Dic467D4semidirect
72. C2×D467#41semidirect
86. C467#525semidirect
91. #123D467semidirect
116. C4⋊C4C2×D467semidirect
122. C22⋊C4C2×D467semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#214187422
C22×C4×D4672
#284179362
#284179312
#284179262
#284179232
#284179212
#284179152
(C22⋊D467)⋊C42
#284179092
#123×C4672
#525467